Why does it seem like so few of the songs from the Minecraft soundtrack ever actually play?

C418 has written a lot of Minecraft music, but only some of it was made to be in Minecraft. A significant minority of the tracks on the albums Minecraft - Volume Alpha and Minecraft - Volume Beta are not from the game and were created for the albums.

You have to admit, if C418 released Minecraft - Volume Alpha with only the tracks that were in the game at the time, it would be a disappointingly familiar album and unexciting news. Instead, he recorded more music available exclusively on that album, and made the album that much more worth buying. This is even mentioned on the wiki:

Minecraft - Volume Alpha is the first soundtrack released for Minecraft by C418, which features all of the songs available since Alpha made by him plus some extras.

C418 did the same when recording Volume Beta — more tracks were created than just those that appeared in the game at the time.